Boundary Value Problems 
Volume 2007 (2007), Article ID 35825, 28 pages
doi:10.1155/2007/35825
Research Article

Interior Gradient Estimates for Nonuniformly Parabolic Equations II

Gary M. Lieberman

 Department of Mathematics, Iowa State University, Ames 50011, IA, USA
Received 31 May 2006; Revised 6 November 2006; Accepted 9 November 2006

Recommended by Vincenzo Vespri

Abstract

We prove interior gradient estimates for a large class of parabolic equations in divergence form. Using some simple ideas, we prove these estimates for several types of equations that are not amenable to previous methods. In particular, we have no restrictions on the maximum eigenvalue of the coefficient matrix and we obtain interior gradient estimates for so-called false mean curvature equation.